Browsing by Author "Abdullahi Yusuf"

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    A Mathematical Model Analysis of Meningitis with Treatment and Vaccination in Fractional Derivatives
    (Springer Science and Business Media LLC, 2022-04-26) Olumuyiwa James Peter; Abdullahi Yusuf; Mayowa M. Ojo; Sumit Kumar; Nitu Kumari; Festus Abiodun Oguntolu
    In this paper, we develop a new mathematical model based on the Atangana Baleanu Caputo (ABC) derivative to investigate meningitis dynamics. We explain why fractional calculus is useful for modeling real-world problems. The model contains all of the possible interactions that cause disease to spread in the population. We start with classical differential equations and extended them into fractional-order using ABC. Both local and global asymptotic stability conditions for meningitis-free and endemic equilibria are determined. It is shown that the model undergoes backward bifurcation, where the locally stable disease-free equilibrium coexists with an endemic equilibrium. We also find conditions under which the model’s disease-free equilibrium is globally asymptotically stable. The approach of fractional order calculus is quite new for such a biological phenomenon. The effects of vaccination and treatment on transmission dynamics of meningitis are examined. These findings are based on various fractional parameter values and serve as a control parameter for identifying important disease-control techniques. Finally, the acquired results are graphically displayed to support our findings.
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    Fractional order of pneumococcal pneumonia infection model with Caputo Fabrizio operator
    (Elsevier BV, 2021-10) Olumuyiwa James Peter; Abdullahi Yusuf; Kayode Oshinubi; Festus Abiodun Oguntolu; John Oluwasegun Lawal; Adesoye Idowu Abioye; Tawakalt Abosede Ayoola
    In this study, we present the Pneumococcal Pneumonia infection model using fractional order derivatives in the Caputo-Fabrizio sense. We use fixed-point theory to prove the existence of the solution and investigate the uniqueness of the model variables. The fractional Adams-Bashforth method is used to compute an iterative solution to the model. Finally, using the model parameter values to explain the importance of the arbitrary fractional order derivative, the numerical results are presented.